My best friend has been spending time with my ex-girlfriend and hasn’t said anything to me about it. I only found out through a mutual friend, and it felt like a betrayal because he knows how much she hurt me. When I confronted him, he said he hadn’t told me precisely because he didn’t want to upset me. He added that he has an independent friendship with her and would like to maintain it despite what went wrong between us. I am torn by this because while I accept that he has a right to be friends with anyone, he also has an obligation to consider my feelings. This has caused a rift between us, and I don’t know if I am in the wrong. What should I do?
Your friend does have the right to be friends with anyone, but you’re also allowed to be hurt by what feels like a betrayal. It may not be easy for you, but he has weighed his options and made a choice based on what he thinks matters to him. You may have to do the same thing and evaluate whether having him in your life is more important than who he chooses to be friends with. This may be difficult, of course, but you will have to hope that time makes it easier for you to manage your feelings. Being friends with someone you don’t like isn’t a crime, unless it leads to something that causes you genuine pain. Give it some time, try and see if 
his friendship with your ex affects you in any way, and examine your priorities again based on how feel a few months from now.

Is it normal for two people to argue all the time if they are engaged and meant to marry within a few months?
Arguments are normal if they lead to constructive criticism and help the relationship evolve. If they don’t lead to anything but pain on both sides, you may have a problem and should consider relationship counselling.